A. 240

B. 200

C. 180

D. 150

It is mentioned in the problem that a total of 180 are learning History.

Now, 180 are learning History and 80 are learning both the subjects. This means that 180 – 80 = 100 are learning only History.

So, out of a total of 300 students, 100 are learning only history which clearly means that rest 200 are learning Geography (whether only geography or with history)

Therefore, total number of students learning Geography = 200.

A. 80

B. 160

C. 120

D. 240

Using the formula: n(A∪B) = n(A) + n(B) – n(A∩B)

n(A∪B) = 160 + 120 – 40 = 240

A. 75

B. 90

C. 120

D. 45

Let B be the set of people who know how to operate machine 2

Let C be the set of people who know how to operate machine 3

A∪B∪C = A + B + C - (A n B + B n C + C n A) + (A n B n C)

240 = 195 + 180 + 165 – ( 120 + 125 + 130) + x

X = 75

A. 200

B. 90

C. 150

D. 900

AUBUC = A + B + C - (A n B + B n C + C n A) + (A n B n C)

We can see that x + x + x + 80 + 200 + 200 + 150 + 100 = 1000

⇒ 3x = 1000 – 730

⇒ x = 270/3 = 90

A. 16

B. 17

C. 18

D. 20

Let B be the set of people who passed in Hindi

Let C be the set of people who passed in Punjabi

A∪B∪C = A + B + C - (A n B + B n C + C n A) + (A n B n C)

120 = 40 + 60 + 40 -10-12-15 + x

X = 120 – 103

X = 17

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A. 29

B. 21

C. 41

D. 27

A is the set of people who chose Ice Tea = 60

B is the set of those who chose Ice Cream = 24

C is the set of those who chose Cold Coffee = 17.

So, AUBUC = 60 + 24 + 17 - (12 + 8 + 3) + 1 = 79.

Number of people who selected none of the 3 items = 120 - 79 = 41.

A. 50

B. 30

C. 20

D. 38

The total number of persons = 400.

Number of candidates who owned at least 1 of the 3 objects = A ∪ B ∪ C, where A is the set of people who owned a four wheeler, B is the set of those who owned a debit card and C is the set of those who owned a wrist watch.

As A∪B∪C = A + B + C - {A n B + B n C + C n A} + A n B n C. So, A∪B∪C = 200 + 140 + 280 - {80 + 60 + 120} + 20

Or A∪B∪C = 380.

380 candidates who attended the interview had at least one of the three gadgets, so 400 - 380 = 20 candidates had none of three objects.

A. 20

B. 25

C. 30

D. 40

Let B be the set of people who opted for Verbal Course

AUB = A + B - (A n B)

x = 180 + 150 -50

x = 280

So, out of 300 students, 280 of them have opted for something or other. Therefore, 20 students have opted for none of the subjects.

Suggested Action:

A. 60

B. 20

C. 36

D. 56

So, (A ∪ B) is the set of students who enrolled for at least one of the two languages. As the students of the class have enrolled for at least one of the two languages, so A ∪ B = 80

A ∪ B = A + B - (A n B)

i.e, 80 = A + 44 - 24

or A = 60 which is the set of students who enrolled for French and includes those who enrolled for both the languages.

But, we need to find out the number of students who enrolled for French only= Students enrolled for French - Students enrolled for both French & Spanish.

= 60 - 24 = 36

A. 5%

B. 25%

C. 10%

D. 15%

Note:

(A ∪ B) = A + B - (A n B) => (A ∪ B) = 40 + 70 - 15 = 95%

95% of the total students study at least one of the two subjects- Accountancy or Business Studies.

So, the remaining (100 - 95)% = 5% of the total students do not study either of the two subjects.